15 19 26 triangle

Obtuse scalene triangle.

Sides: a = 15   b = 19   c = 26

Area: T = 140.7122472795
Perimeter: p = 60
Semiperimeter: s = 30

Angle ∠ A = α = 34.7288341173° = 34°43'42″ = 0.60661238972 rad
Angle ∠ B = β = 46.18769385396° = 46°11'13″ = 0.80661141489 rad
Angle ∠ C = γ = 99.08547202874° = 99°5'5″ = 1.72993546074 rad

Height: ha = 18.76216630393
Height: hb = 14.81218392415
Height: hc = 10.82440363688

Median: ma = 21.5
Median: mb = 18.98802528961
Median: mc = 11.13655287257

Inradius: r = 4.69904157598
Circumradius: R = 13.1655144235

Vertex coordinates: A[26; 0] B[0; 0] C[10.38546153846; 10.82440363688]
Centroid: CG[12.12882051282; 3.60880121229]
Coordinates of the circumscribed circle: U[13; -2.07987069845]
Coordinates of the inscribed circle: I[11; 4.69904157598]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 145.2721658827° = 145°16'18″ = 0.60661238972 rad
∠ B' = β' = 133.813306146° = 133°48'47″ = 0.80661141489 rad
∠ C' = γ' = 80.91552797126° = 80°54'55″ = 1.72993546074 rad

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How did we calculate this triangle?

Now we know the lengths of all three sides of the triangle and the triangle is uniquely determined. Next we calculate another its characteristics - same procedure as calculation of the triangle from the known three sides SSS.

a = 15 ; ; b = 19 ; ; c = 26 ; ;

1. The triangle circumference is the sum of the lengths of its three sides

p = a+b+c = 15+19+26 = 60 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 60 }{ 2 } = 30 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 30 * (30-15)(30-19)(30-26) } ; ; T = sqrt{ 19800 } = 140.71 ; ;

4. Calculate the heights of the triangle from its area.

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 140.71 }{ 15 } = 18.76 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 140.71 }{ 19 } = 14.81 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 140.71 }{ 26 } = 10.82 ; ;

5. Calculation of the inner angles of the triangle using a Law of Cosines

a**2 = b**2+c**2 - 2bc cos( alpha ) ; ; alpha = arccos( fraction{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 15**2-19**2-26**2 }{ 2 * 19 * 26 } ) = 34° 43'42" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 19**2-15**2-26**2 }{ 2 * 15 * 26 } ) = 46° 11'13" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-15**2-19**2 }{ 2 * 19 * 15 } ) = 99° 5'5" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 140.71 }{ 30 } = 4.69 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 15 }{ 2 * sin 34° 43'42" } = 13.17 ; ;




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